Problem: Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area. 

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

<image> Illustration to the first example.

Input

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).

Output

The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold. 

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

3 2


Output

1.154700538379 1.632993161855


Input

2 100000


Output

70710.678118654752

Note

Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  double n, h, viv = 0.0;
  int i;
  cin >> n >> h;
  double ans = 0;
  double area = h / 2;
  double low = 0.0;
  double high = 1000010.0;
  int cnt = 150;
  while (cnt--) {
    double mid = (low + high) / 2;
    double h2 = mid;
    double b2 = mid / h;
    double a2 = h2 * b2 / 2;
    if (n * a2 >= area) {
      viv = a2;
      ans = mid;
      high = mid - 0.000001;
    } else {
      low = mid + 0.000001;
    }
  }
  printf("%0.15f ", ans);
  for (i = 1; i < n - 1; i++) {
    double ans1 = 0.0;
    double up_surface = h - ans;
    double low = 0.0;
    double high = up_surface;
    int cnt = 150;
    while (cnt--) {
      double mid = (low + high) / 2;
      double hh = up_surface - mid;
      double aa = (h - up_surface) / h;
      double bb = (h - mid) / h;
      double a2 = (aa + bb) / 2;
      a2 = a2 * hh;
      if (a2 <= viv) {
        ans1 = mid;
        high = mid - 0.000001;
      } else {
        low = mid + 0.000001;
      }
    }
    printf("%0.15f ", h - ans1);
    ans = h - ans1;
  }
}